Simplify the following expression: $ a = \dfrac{-6}{5z - 3} - \dfrac{-9}{4} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-6}{5z - 3} \times \dfrac{4}{4} = \dfrac{-24}{20z - 12} $ Multiply the second expression by $\dfrac{5z - 3}{5z - 3}$ $ \dfrac{-9}{4} \times \dfrac{5z - 3}{5z - 3} = \dfrac{-45z + 27}{20z - 12} $ Therefore $ a = \dfrac{-24}{20z - 12} - \dfrac{-45z + 27}{20z - 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-24 - (-45z + 27) }{20z - 12} $ Distribute the negative sign: $a = \dfrac{-24 + 45z - 27}{20z - 12}$ $a = \dfrac{45z - 51}{20z - 12}$